Estimator performance for a class of nonlinear estimation problems

The state estimation problem for a certain class of nonlinear stochastic systems with white Gaussian plant and observation noise is considered. The optimal (minimum variance) estimators for these systems are recursive and finite dimensional. A particular nonlinear system which contains a polynomial nonlinearity is presented. Both optimal and suboptimal estimators and an estimation lower bound for such a system are derived. The performance of the optimal and suboptimal estimators and the lower bound are compared both analytically and by computer simulation.